The figure shows the top left-hand corner of the complete diagram and we see by symmetry that the perpendicular from the corner to short side of the rectangle has length

\frac{1}{2}

. Thus the diagonal of the square may be divided into three sections of length

\frac{1}{2}

x

and

\frac{1}{2}

respectively.

The length of this diagonal $= \sqrt{10^{2} + 10^{2}} = \sqrt{200} = 10 \sqrt{2}$ , so $x = 10 \sqrt{2} - 1$ .